Question

which explains how to find the radius of a circle whose equation is in the form ( x^{2}+y^{2}=z )?
the radius is the constant term, ( z ).
the radius is the constant term, ( z ), divided by 2.
the radius is the square root of the constant term, ( z ).
the radius is the square of the constant term, ( z ).

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - a)^2+(y - b)^2=r^2\), where \((a,b)\) is the center and \(r\) is the radius.

Step2: Analyze the given equation \(x^{2}+y^{2}=z\)

In the equation \(x^{2}+y^{2}=z\), it can be rewritten as \((x - 0)^2+(y - 0)^2=z\). Comparing with the standard form \((x - a)^2+(y - b)^2=r^2\), we have \(r^{2}=z\).

Step3: Solve for \(r\)

To find \(r\), take the square root of both sides of the equation \(r^{2}=z\). So \(r=\sqrt{z}\) (since radius \(r>0\)).

Answer:

The radius is the square root of the constant term, \(z\).